On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

<p/> <p>As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this...

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Main Authors: Erzakova Nina A, Santana Sergio Falcon, Appell J&#252;rgen, V&#228;th Martin
Format: Article
Language:English
Published: SpringerOpen 2004-01-01
Series:Fixed Point Theory and Applications
Online Access:http://www.fixedpointtheoryandapplications.com/content/2004/719153
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spelling doaj-762b11345ebb4aa8819f96d7fd8c4fef2020-11-24T23:34:35ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122004-01-0120044719153On some Banach space constants arising in nonlinear fixed point and eigenvalue theoryErzakova Nina ASantana Sergio FalconAppell J&#252;rgenV&#228;th Martin<p/> <p>As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.</p>http://www.fixedpointtheoryandapplications.com/content/2004/719153
collection DOAJ
language English
format Article
sources DOAJ
author Erzakova Nina A
Santana Sergio Falcon
Appell J&#252;rgen
V&#228;th Martin
spellingShingle Erzakova Nina A
Santana Sergio Falcon
Appell J&#252;rgen
V&#228;th Martin
On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
Fixed Point Theory and Applications
author_facet Erzakova Nina A
Santana Sergio Falcon
Appell J&#252;rgen
V&#228;th Martin
author_sort Erzakova Nina A
title On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
title_short On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
title_full On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
title_fullStr On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
title_full_unstemmed On some Banach space constants arising in nonlinear fixed point and eigenvalue theory
title_sort on some banach space constants arising in nonlinear fixed point and eigenvalue theory
publisher SpringerOpen
series Fixed Point Theory and Applications
issn 1687-1820
1687-1812
publishDate 2004-01-01
description <p/> <p>As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.</p>
url http://www.fixedpointtheoryandapplications.com/content/2004/719153
work_keys_str_mv AT erzakovaninaa onsomebanachspaceconstantsarisinginnonlinearfixedpointandeigenvaluetheory
AT santanasergiofalcon onsomebanachspaceconstantsarisinginnonlinearfixedpointandeigenvaluetheory
AT appellj252rgen onsomebanachspaceconstantsarisinginnonlinearfixedpointandeigenvaluetheory
AT v228thmartin onsomebanachspaceconstantsarisinginnonlinearfixedpointandeigenvaluetheory
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